I really like dogs, although I do not own one. I have no issue with a person owning a dog, particularly as I agree they can make fabulous additions to families and comfort to kids.
But, the issue of dog mess where I live has reached ridiculous levels and as the OP puts it you do have to walk looking down to avoid stepping in it.
I live near to a place that has been created as a walking/cycling space. It is used by many people, including dog walkers. It is literally festooned with crap. I have to weave through it when I run. No way could you take a push chair there or kids on bikes. It is a year old and has umpteen poo bins which I can attest are emptied daily. I see dogs crap and the owner pretend they couldn't see where so don't collect it. I have been known to walk them to the steaming, stinking spot.
I live in a nice part of our town. All along the route the children of several schools take the pavement is studded with dog mess. Also all along the route on walls and ends of driveways are little plastic bags filled with dog mess that has been picked up and deposited by the owner because they just cannot be arsed to take it home.
There is a park near us, beautiful green space/playground, boating lake where the kids cannot play on the massive expanse of grass because it's peppered with dog mess.
At Tankerton a few weeks ago on a sunny, Sunday afternoon DS age 4 was playing on the beach rolling his fire engine along the breaker. We had to leave in a hurry as the mud on the breaker was in fact a pile of dog mess.
A friend routinely has a dog crap at the end of her drive, as she pulls back it catches in her gyres and gets smeared right across the footpath. She has two small DC and lives opposite a junior school.
Many, many dog owners are responsible, but many, many are not. It cannot conceivably be just a minority, as a minority cannot fill a park.
I am urging my council to set up a website where you can send photos if the dog walker (note not the animal, it's doing what animals do). The owners should have their fisog published so their neighbours know it's them allowing their open spaces to become uninhabitable.
In the meantime I simply don't see why dogs cannot be on leads, and the owners fined up the ying yang on the spot if they don't pick up. With the sheer weight of shit involved it would be a self-funding exercise.